Simplify the following expression: $z = \dfrac{2a + 6}{3a + 5} \div 9$
Solution: Dividing by a number is the same as multiplying by its inverse. $z = \dfrac{2a + 6}{3a + 5} \times \dfrac{1}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{(2a + 6) \times 1} {(3a + 5) \times 9}$ $z = \dfrac{2a + 6}{27a + 45}$